Systemic risk and network intervention

TL;DR

This paper introduces a novel adversarial network protection framework, analytically solving for optimal interventions in network equilibria with applications across various fields, revealing waterfilling-like solutions related to Bonacich centrality.

Contribution

It formulates a min-max problem for network protection, providing analytical solutions for specific aggregate performance measures and linking optimal protection strategies to network centrality.

Findings

Optimal protection concentrates on specific nodes based on the performance measure.

Solutions exhibit a waterfilling structure, depending on the aggregate performance.

Protection strategies relate to Bonacich centrality measures.

Abstract

We consider a novel adversarial shock/protection problem for a class of network equilibria models emerging from a variety of different fields as continuous network games, production networks, opinion dynamic models. The problem is casted into a min-max problem and analytically solved for two particular cases of aggregate performances: the mean square of the equilibrium or of its arithmetic mean. The main result is on the shape of the solutions, typically exhibiting a waterfilling type structure with the optimal protection concentrated in a proper subset of the nodes, depending significantly on the aggregate performance considered. The relation of the optimal protection with the Bonacich centrality is also considered.